Be warned, I'm a total plant newbie!
Anyway, she recommended I get:
-a couple anubias, she said the nana petite and the var. nana narrow leaf would be best.
-couple dwarf lilies (they're so pretty!)
-couple java ferns (I like the lace ones)

I'm likely going to order some christmas moss, too.

But, all of these plants are slow growers--good, so I don't have to trim so much, but bad if they don't eat much fish waste...
Is there any recommendations on a fast growing plant (that doesn't shed) that'd fit in the Hawkeye, one that is easy to care for? And is my current selection of plants the right amount for the tank size?

Been doing a ton of research for the last month--my betta's currently in a 2.5gal critter carrier (heated), and I cannot wait to see what he'll think of his new tank once it's finished. I'm hoping to put in a couple ghost shrimp as well, since he's a pretty passive fishy. I've heard people can keep cories in a tank this size, but aren't 5gals too small for them? I'd love to grab a couple of those instead of shrimp, if it was possible...

Generally speaking, cories (you need at least 3 or 4) and a betta would be overstocking a 5 gal tank so I wouldnt reccomend it :/

Fast growing plants:
-Hygrophila. I bought mine in a tube from petco. It was tiny! now its huge! The leaves are a beautiful shade of green. I also love how it "blooms" at night the top leaves close, and during the day they open up - it really is quite nice. heres a pic of mine a few weeks ago. Its a few inches taller now, has more levaes and the lower leaves are getting big.

Another good plant I have heard about is wisteria. I have that too but Its still new and hast grown much. It can be left floating too, your betta will love it. This is what it looks like:

Hornwort is supposed to grow like a weed and its beautiful. Though I hear it sheds needles like crazy. Im probably still gonna try it tho :P

To trim these plants you simply pull it from the substrate, cut the bottom part off and replant the tops. Its easier for the plant to grow roots than have to grow a whole new head of leaves. And that way you always get the "new" leaves :P